In cellular base stations, satellite communications and other communications and broadcast systems, many radio frequency (RF) carriers, spread over a large bandwidth, are amplified simultaneously in the same high power amplifier. For the power amplifier this has the effect that the instantaneous transmit power will vary very widely and very rapidly. This is because the sum of many independent RF carriers (i.e. a multi-carrier signal) tends to have a large peak-to-average power ratio. It also tends to have a similar amplitude distribution as bandpass filtered Gaussian noise, which has a Rayleigh distribution.
The main difficulties in a PA are efficiency and linearity. A conventional class B power amplifier exhibits maximum DC to RF power conversion efficiency when it delivers its peak power to the load. Since the quasi-Rayleigh distribution of amplitudes in the summed transmit signal implies a large difference between the average power and the peak power, the overall efficiency when amplifying such a signal in a conventional class B amplifier is very low. For a quasi-Rayleigh distributed signal with a 10 dB peak-to-average power ratio, the efficiency of an ideal class B amplifier is only 28%, see [1].
The linearity of an RF power amplifier is usually characterized by its AM—AM (AM=amplitude modulation) and AM-PM (PM=phase modulation) distortion characteristics. Non-linearities manifest themselves as cross-mixing of different parts of the signal, leading to leakage of signal energy into undesired frequency bands. By restricting the output signal to a smaller part of the total voltage swing of the power amplifier, the linearity can be increased. However, this reduces the efficiency of the amplifier even further. The linearity of a power amplifier is also greatly reduced if the amplifier saturates (the output voltage is clipped). This means that it is not possible to increase efficiency by driving the amplifier into saturation, since the distortion will then reach unacceptable levels.
One way of increasing the efficiency of an RF power amplifier is to use the Doherty principle [1, 2, 3]. The Doherty amplifier uses in its basic form two amplifier stages, a main and an auxiliary amplifier (also called carrier and peaking amplifier, respectively). The load is connected to the auxiliary amplifier, and the main amplifier is connected to the load through an impedance-inverter, usually a quarter wavelength transmission line or an equivalent lumped network.
At low output levels only the main amplifier is active, and the auxiliary amplifier is shut off. In this region, the main amplifier sees a higher (transformed) load impedance than the impedance at peak power, which increases its efficiency in this region. When the output level climbs over the so-called transition point (usually at half the maximum output voltage), the auxiliary amplifier becomes active, driving current into the load. Through the impedance-inverting action of the quarter wavelength transmission line, this decreases the effective impedance at the output of the main amplifier, such that the main amplifier is kept at a constant (peak) voltage above the transition point. The result is a substantially linear output to input power relationship, with a significantly higher efficiency than a traditional amplifier.
The transition point can be shifted, so that the auxiliary amplifier kicks in at a lower or higher power level. This can be used for increasing efficiency for a specific type of signal or a specific amplitude distribution. When the transition point is shifted, the power division between the amplifiers at peak power is shifted accordingly, and the average power loss in each amplifier also changes. The latter effect also depends on the specific amplitude distribution.
The Doherty concept has also been extended to multi-stage (more than one auxiliary amplifier) variants [1, 4, 5]. This allows the efficiency to be kept high over a broader range of output power levels and varying amplitude distributions. Alternatively, the average efficiency for a specific amplitude distribution and a specific power level can be made higher.
The original Doherty amplifier used a quarter wavelength transmission line coupled directly between the outputs of the two amplifiers. However, state of the art RF power transistors require a very low load impedance, which means that the quarter wavelength transmission line for the original Doherty configuration also has to be designed at a correspondingly low impedance. A solution for this problem is given in [3] and [6] and used in [7]. This solution places the impedance inverter between higher impedance points, obtained through single or multiple quarter wavelength impedance transformers.
The Doherty amplifiers are known to be non-linear, and to have a linearity “inversely proportional to their efficiency” [7], especially outside a narrow frequency band. Attempts have been made to reduce the distortion and increasing the useful bandwidth by paralleling multiple Doherty amplifiers with different impedance inverter center frequencies, different bias for the auxiliary amplifiers and different matching structures, in order to “randomize” the inter-modulation products as much as possible [7]. This technique also involves complicated trimming of bias levels.
Detailed analysis shows that a Doherty amplifier, even when made from ideal components, is non-linear for all but very narrow frequency bands. The results further show that losses, that would not affect linearity in a regular class B, A or AB amplifier, cause severe non-linearity in a Doherty amplifier. Furthermore, losses can decrease efficiency more in a Doherty amplifier than a regular amplifier (although the resultant efficiency is still higher for the Doherty), since they can cause the main amplifiers to work non-optimally in addition to just adding losses. A more detailed discussion of these effects will be given below.
Another important feature is that Doherty amplifiers are inherently band-limited, since the impedance inverting network only provides 90 degrees of phase shift at a single frequency. This band-limiting has several effects.
One important effect is that the output is distorted at frequencies away from the center frequency. This effect, which severely limits the use of the Doherty amplifier in wideband linear applications, is due to the growing (chiefly reactive in the lossless case) impedance of the quarter wavelength network at frequencies away from the center frequency. This distortion is present even if all components are linear and lossless, since it is due to the reflection (because of the non-zero impedance) of the non-linear current from the auxiliary amplifier at the impedance inverter. The resulting voltage shows up as a strongly frequency-dependent non-linear component in the amplified output signal.
Another effect is that the Doherty principle, i.e. the suppression of RF voltage rise at the main amplifier above a certain transition point, works poorly outside a limited frequency band. This is because the suppression requires the voltages from the main amplifier and the auxiliary amplifier to be in perfect anti-phase at the output of the main amplifier. Since the quarter-wave network is really only a quarter wave (90 degrees) phase shift at the center frequency, and shorter or longer at frequencies below and above the center frequency, respectively, this requirement gets more and more violated the further one gets from the center frequency of the impedance inverter.
Furthermore, the output signal is bandpass filtered through reflections from the quarter-wave network.
Losses in the transistors, impedance inverters and the DC feed networks also give rise to unexpected distortion. This is because these losses make the impedance at the impedance inverter, as seen from the auxiliary amplifier, resistive instead of the ideal short-circuit (a lossless quarter wavelength transmission line loaded with the infinite impedance of a current generator is a short-circuit at center frequency). A finite resistance at the output of the main amplifier, as well as losses in the quarter-wave network will cause distortion. The distortion in the output caused by these losses are due to the same type of reflection (but now resistive instead of reactive) of the non-linear current from the auxiliary amplifier at the impedance inverter which causes the frequency-dependent distortion mentioned earlier.
Losses will also possibly further decrease efficiency, since the voltage at the main amplifier will not be at its maximum at output levels above the transition point. By providing more current from the main amplifier, this problem can be reduced. The voltage at the main amplifier will then instead be governed by saturation, which will lead to non-linearity in the output. By carefully adjusting the transition point and output current from the auxiliary amplifier (by adjusting the bias level and gain of the drive signal) the output can again be made more linear (at least decreasing the amplitude distortion). This last effect is due to the increased impedance at the output of the auxiliary amplifier, which makes the auxiliary amplifier contribute more voltage to the output for each unit of current provided. The trimming method just described only works in a narrow band and is not easily reproducible since it involves using the saturation non-linearity, whose exact shape now becomes important. Due to non-linear coupling to generated overtones it can also give a high and unpredictable AM-PM distortion.
The non-linear characteristic of the regular Doherty amplifier built and optimized with the techniques mentioned is highly complex. It is a non-linearity whose AM—AM and AM-PM distortion varies strongly with frequency and has a frequency (filter) characteristic that varies non-linearly with amplitude. This makes it very difficult to compensate for by applying pre-distortion. Since the pre-distorter would have to be very complex (and hence implemented with digital signal processing techniques), and a pre-distorter has to have a rather wide bandwidth compared to the already distortion-widened signal it should compensate for (since the inverse function to the distortion function is of higher order than the distortion function itself, such a pre-distorter would be hard to build even for moderately wideband signals.
The conclusion is that the current way of building Doherty amplifiers can only provide reasonable linear performance and efficiency in a narrow band, and this only by relying on saturation effects in the main amplifier. Furthermore, the nonlinear characteristic is not easily compensated for in a wide band by using pre-distortion.